Geodesic
On a Result of Telyakovskii and Multiple Hilbert Transforms with Polynomial Phases
Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 242-256

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In this paper, we prove a multiple analog of the theorem proved by Arkhipov and the author in 1987, which provides an estimate for the discrete Hilbert transform with polynomial phase. For the linear case, the corresponding estimates of the sum of multiple trigonometric series was proved by Telyakovskii. 
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     author = {K. I. Oskolkov},
     title = {On a {Result} of {Telyakovskii} and {Multiple} {Hilbert} {Transforms} with {Polynomial} {Phases}},
     journal = {Matemati\v{c}eskie zametki},
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K. I. Oskolkov. On a Result of Telyakovskii and Multiple Hilbert Transforms with Polynomial Phases. Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 242-256. http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a6/